47 ideas
| 1502 | Parmenides was much more cautious about accepting ideas than his predecessors [Simplicius on Parmenides] |
| Full Idea: Parmenides would not agree with anything unless it seemed necessary, whereas his predecessors used to come up with unsubstantiated assertions. | |
| From: comment on Parmenides (fragments/reports [c.474 BCE], A28) by Simplicius - On Aristotle's 'Physics' 9.116.2- | |
| A reaction: from Eudemus |
| 13838 | A decent modern definition should always imply a semantics [Hacking] |
| Full Idea: Today we expect that anything worth calling a definition should imply a semantics. | |
| From: Ian Hacking (What is Logic? [1979], §10) | |
| A reaction: He compares this with Gentzen 1935, who was attempting purely syntactic definitions of the logical connectives. |
| 13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
| Full Idea: 'Dilution' (or 'Thinning') provides an essential contrast between deductive and inductive reasoning; for the introduction of new premises may spoil an inductive inference. | |
| From: Ian Hacking (What is Logic? [1979], §06.2) | |
| A reaction: That is, inductive logic (if there is such a thing) is clearly non-monotonic, whereas classical inductive logic is monotonic. |
| 13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
| Full Idea: If A |- B and B |- C, then A |- C. This generalises to: If Γ|-A,Θ and Γ,A |- Θ, then Γ |- Θ. Gentzen called this 'cut'. It is the transitivity of a deduction. | |
| From: Ian Hacking (What is Logic? [1979], §06.3) | |
| A reaction: I read the generalisation as 'If A can be either a premise or a conclusion, you can bypass it'. The first version is just transitivity (which by-passes the middle step). |
| 13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
| Full Idea: Only the cut rule can have a conclusion that is less complex than its premises. Hence when cut is not used, a derivation is quite literally constructive, building up from components. Any theorem obtained by cut can be obtained without it. | |
| From: Ian Hacking (What is Logic? [1979], §08) |
| 16951 | It was realised that possible worlds covered all modal logics, if they had a structure [Dummett] |
| Full Idea: The new discovery was that with a suitable structure imposed on the space of possible worlds, the Leibnizian idea would work for all modal logics. | |
| From: Michael Dummett (Could There Be Unicorns? [1983], 1) |
| 16952 | If something is only possible relative to another possibility, the possibility relation is not transitive [Dummett] |
| Full Idea: If T is only possible if S obtains, and S is possible but doesn't obtain, then T is only possible in the world where S obtains, but T is not possible in the actual world. It follows that the relation of relative possibility is not transitive. | |
| From: Michael Dummett (Could There Be Unicorns? [1983], 1) | |
| A reaction: [compressed] |
| 16953 | Relative possibility one way may be impossible coming back, so it isn't symmetrical [Dummett] |
| Full Idea: If T is only possible if S obtains, T and S hold in the actual world, and S does not obtain in world v possible relative to the actual world, then the actual is not possible relative to v, since T holds in the actual. Accessibility can't be symmetrical. | |
| From: Michael Dummett (Could There Be Unicorns? [1983], 1) |
| 16960 | If possibilitiy is relative, that might make accessibility non-transitive, and T the correct system [Dummett] |
| Full Idea: If some world is 'a way the world might be considered to be if things were different in a certain respect', that might show that the accessibility relation should not be taken to be transitive, and we should have to adopt modal logic T. | |
| From: Michael Dummett (Could There Be Unicorns? [1983], 8) | |
| A reaction: He has already rejected symmetry from the relation, for reasons concerning relative identity. He is torn between T and S4, but rejects S5, and opts not to discuss it. |
| 16958 | In S4 the actual world has a special place [Dummett] |
| Full Idea: In S4 logic the actual world is, in itself, special, not just from our point of view. | |
| From: Michael Dummett (Could There Be Unicorns? [1983], 8) | |
| A reaction: S4 lacks symmetricality, so 'you can get there, but you can't get back', which makes the starting point special. So if you think the actual world has a special place in modal metaphysics, you must reject S5? |
| 13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
| Full Idea: I don't believe English is by nature classical or intuitionistic etc. These are abstractions made by logicians. Logicians attend to numerous different objects that might be served by 'If...then', like material conditional, strict or relevant implication. | |
| From: Ian Hacking (What is Logic? [1979], §15) | |
| A reaction: The idea that they are 'abstractions' is close to my heart. Abstractions from what? Surely 'if...then' has a standard character when employed in normal conversation? |
| 13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
| Full Idea: First-order logic is the strongest complete compact theory with a Löwenheim-Skolem theorem. | |
| From: Ian Hacking (What is Logic? [1979], §13) |
| 13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
| Full Idea: Henkin proved that there is no first-order treatment of branching quantifiers, which do not seem to involve any idea that is fundamentally different from ordinary quantification. | |
| From: Ian Hacking (What is Logic? [1979], §13) | |
| A reaction: See Hacking for an example of branching quantifiers. Hacking is impressed by this as a real limitation of the first-order logic which he generally favours. |
| 13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
| Full Idea: Second-order logic has no chance of a completeness theorem unless one ventures into intensional entities and possible worlds. | |
| From: Ian Hacking (What is Logic? [1979], §13) |
| 13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
| Full Idea: My doctrine is that the peculiarity of the logical constants resides precisely in that given a certain pure notion of truth and consequence, all the desirable semantic properties of the constants are determined by their syntactic properties. | |
| From: Ian Hacking (What is Logic? [1979], §09) | |
| A reaction: He opposes this to Peacocke 1976, who claims that the logical connectives are essentially semantic in character, concerned with the preservation of truth. |
| 13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
| Full Idea: For some purposes the variables of first-order logic can be regarded as prepositions and place-holders that could in principle be dispensed with, say by a system of arrows indicating what places fall in the scope of which quantifier. | |
| From: Ian Hacking (What is Logic? [1979], §11) | |
| A reaction: I tend to think of variables as either pronouns, or as definite descriptions, or as temporary names, but not as prepositions. Must address this new idea... |
| 13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
| Full Idea: A Löwenheim-Skolem theorem holds for anything which, on my delineation, is a logic. | |
| From: Ian Hacking (What is Logic? [1979], §13) | |
| A reaction: I take this to be an unusually conservative view. Shapiro is the chap who can give you an alternative view of these things, or Boolos. |
| 448 | No necessity could produce Being either later or earlier, so it must exist absolutely or not at all [Parmenides] |
| Full Idea: What necessity impelled Being, if it did spring from nothing, to be produced later or earlier? Thus it must be absolutely, or not at all. | |
| From: Parmenides (fragments/reports [c.474 BCE], B08 ll.?), quoted by Simplicius - On Aristotle's 'Physics' 9.145.1- |
| 447 | Being must be eternal and uncreated, and hence it is timeless [Parmenides] |
| Full Idea: Being has no coming-to-be and no destruction, for it is whole of limb, without motion, and without end. And it never was, nor will be, because it is now, a whole all together, one, continuous; for what creation of it will you look for? | |
| From: Parmenides (fragments/reports [c.474 BCE], B08 ll.?), quoted by Simplicius - On Aristotle's 'Physics' 9.145.1- |
| 449 | Being is not divisible, since it is all alike [Parmenides] |
| Full Idea: Being is not divisible, since it is all alike. | |
| From: Parmenides (fragments/reports [c.474 BCE], B08 ll.?), quoted by Simplicius - On Aristotle's 'Physics' 9.145.1- |
| 1503 | There is no such thing as nothing [Parmenides] |
| Full Idea: There is no such thing as nothing. | |
| From: Parmenides (fragments/reports [c.474 BCE], B06), quoted by Simplicius - On Aristotle's 'Physics' 9.86.27- |
| 445 | The realm of necessary non-existence cannot be explored, because it is unknowable [Parmenides] |
| Full Idea: The other way of enquiry, that IT IS NOT, and IT is bound NOT TO BE, cannot be explored, for you could neither recognise nor express that which IS NOT. | |
| From: Parmenides (fragments/reports [c.474 BCE], B02), quoted by Simplicius - On Aristotle's 'Physics' 9.116.28- |
| 21820 | Parmenides at least saw Being as the same as Nous, and separate from the sensed realm [Parmenides, by Plotinus] |
| Full Idea: Parmenides made some approach to the doctrine of Plato in identifying Being with Intellectual-Principle [Nous] while separating Real Being from the realm of sense. | |
| From: report of Parmenides (fragments/reports [c.474 BCE]) by Plotinus - The Enneads 5.1.08 | |
| A reaction: The point is that for Parmenides the One is the essence of Being, but for platonists there is something prior to and higher than Being. For Plato it is the Good; for Plotinus it is a revised (non-Being) concept of the One. |
| 452 | All our concepts of change and permanence are just names, not the truth [Parmenides] |
| Full Idea: All things that mortals have established, believing in their truth, are just a name: Becoming and Perishing, Being and Not-Being, and change of position, and alteration of bright colour. | |
| From: Parmenides (fragments/reports [c.474 BCE], B08 ll.?), quoted by Simplicius - On Aristotle's 'Physics' 9.145.1- |
| 1504 | Something must be unchanging to make recognition and knowledge possible [Aristotle on Parmenides] |
| Full Idea: Parmenides and Melissus were the first to appreciate that there must be unchanging entities, if recognition and knowledge are to exist. | |
| From: comment on Parmenides (fragments/reports [c.474 BCE], A25) by Aristotle - On the Heavens 298b14 |
| 444 | The first way of enquiry involves necessary existence [Parmenides] |
| Full Idea: The first way of enquiry is the one that IT IS, and it is not possible for IT NOT TO BE, which is the way of credibility, for it follows truth. | |
| From: Parmenides (fragments/reports [c.474 BCE], B02), quoted by Simplicius - On Aristotle's 'Physics' 9.116.28- | |
| A reaction: also Proclus 'Timeus' |
| 450 | Necessity sets limits on being, in order to give it identity [Parmenides] |
| Full Idea: Powerful necessity holds Being in the bonds of a limit, which constrains it round about, because divine law decrees that Being shall not be without boundary. For it is not lacking, but if it were spatially infinite, it would lack everything. | |
| From: Parmenides (fragments/reports [c.474 BCE], B08 ll.?), quoted by Simplicius - On Aristotle's 'Physics' 9.145.1- |
| 16957 | Possible worlds aren't how the world might be, but how a world might be, given some possibility [Dummett] |
| Full Idea: The equation of a possible world with the way that the (actual) world might be is wrong: the way a distant world might be is not a way the world might be, but a way we might allow it to be given how some intervening world might be. | |
| From: Michael Dummett (Could There Be Unicorns? [1983], 8) | |
| A reaction: The point here is that a system of possible worlds must include relative possibilities as well as actual possibilities. Dummett argues against S5 modal logic, which makes them all equal. Things impossible here might become possible. Nice. |
| 16959 | If possible worlds have no structure (S5) they are equal, and it is hard to deny them reality [Dummett] |
| Full Idea: If our space of possible worlds has no structure, as in the semantics for S5, then, from the standpoint of the semantics, all possible worlds are on the same footing; it then becomes difficult to resist the claim that all are equally real. | |
| From: Michael Dummett (Could There Be Unicorns? [1983], 8) | |
| A reaction: This is a rather startling and interesting claim, given that modern philosophy seems full of thinkers who both espouse S5 for metaphysics, and also deny Lewisian realism about possible worlds. I'll ponder that one. Must read the new Williamson…. |
| 451 | Thinking implies existence, because thinking depends on it [Parmenides] |
| Full Idea: To think is the same as the thought that IT IS, for you will not find thinking without Being, on which it depends for its expression. | |
| From: Parmenides (fragments/reports [c.474 BCE], B08 ll.?), quoted by Simplicius - On Aristotle's 'Physics' 9.145.1- |
| 1506 | Parmenides treats perception and intellectual activity as the same [Theophrastus on Parmenides] |
| Full Idea: Parmenides treats perception and intellectual activity as the same. | |
| From: comment on Parmenides (fragments/reports [c.474 BCE], A46) by Theophrastus - On the Senses 3.1 | |
| A reaction: cf Theaetetus pt 1 |
| 3058 | Only reason can prove the truth of facts [Parmenides] |
| Full Idea: Reason alone will prove the truth of facts. | |
| From: Parmenides (fragments/reports [c.474 BCE]), quoted by Diogenes Laertius - Lives of Eminent Philosophers 09.3.3 |
| 16956 | To explain generosity in a person, you must understand a generous action [Dummett] |
| Full Idea: It cannot be explained what it is for a person to be generous without first explaining what it is for an action to be generous. | |
| From: Michael Dummett (Could There Be Unicorns? [1983], 4) | |
| A reaction: I presume a slot machine can't be 'generous', even if it favours the punter, so you can't specify a generous action without making reference to the person. A benign circle, as Aristotle says. |
| 555 | People who say that the cosmos is one forget that they must explain movement [Aristotle on Parmenides] |
| Full Idea: Those who assert that the universe is one and a single nature, when they try to give the causes of generation and destruction, miss out the cause of movement. | |
| From: comment on Parmenides (fragments/reports [c.474 BCE]) by Aristotle - Metaphysics 988b |
| 5081 | There could be movement within one thing, as there is within water [Aristotle on Parmenides] |
| Full Idea: Why does it follow from there being only one thing that it is unmoving, since, for example, water moves internally while remaining one? | |
| From: comment on Parmenides (fragments/reports [c.474 BCE]) by Aristotle - Physics 186a16 | |
| A reaction: One suspects that Parmenides wasn't used to critical questions like this, and would have sharpened up his theory if it had been subjected to criticism. How big was the One? Maybe Aristotle is the real father of philosophy. |
| 1509 | The one can't be divisible, because if it was it could be infinitely divided down to nothing [Parmenides, by Simplicius] |
| Full Idea: Since the one is everywhere alike, then if it is divisible, it will be equally divisible everywhere….so let it be divided everywhere. It is obvious that nothing will remain and the whole will vanish, and so (if it is compound) it is composed of nothing. | |
| From: report of Parmenides (fragments/reports [c.474 BCE]) by Simplicius - On Aristotle's 'Physics' 9.139.5- | |
| A reaction: he is quoting Porphyry |
| 20900 | Defenders of the One say motion needs the void - but that is not part of Being [Parmenides, by Aristotle] |
| Full Idea: Defenders of the One say that there could not be motion without a void, and that void is what does not exist, and that nothing that is not belongs to being. | |
| From: report of Parmenides (fragments/reports [c.474 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 325a26 | |
| A reaction: This is why motion is an illusion, a view also supported by the paradoxes of Zeno of Elea. Aristotle goes on to give Democritus's response to this idea. Parmenides was contemplating 'void', before Democritus got to it. |
| 226 | The one is without any kind of motion [Parmenides] |
| Full Idea: The one is without any kind of motion. | |
| From: Parmenides (fragments/reports [c.474 BCE]), quoted by Plato - Parmenides 139a |
| 1505 | Reason sees reality as one, the senses see it as many [Aristotle on Parmenides] |
| Full Idea: Since he is forced to be guided by appearances, he assumes that the one exists from the viewpoint of reason, but that a plurality exists from the viewpoint of the sense, and so he posits two principles and causes - hot and cold. | |
| From: comment on Parmenides (fragments/reports [c.474 BCE], A24) by Aristotle - Metaphysics 986b27- | |
| A reaction: A profound thought. Empiricists emphasies experience, and end up with fragmented reality. Reason explains experience, and in the process sees the world as unities (like objects), though a single unity is going too far. |
| 453 | Reality is symmetrical and balanced, like a sphere, with no reason to be greater one way rather than another [Parmenides] |
| Full Idea: Since there is a spatial limit, it is complete on every side, like the mass of a well-rounded sphere, equally balanced from its centre in every direction; for it is not bound to be at all either greater or less in this direction or that. | |
| From: Parmenides (fragments/reports [c.474 BCE], B08 ll.?), quoted by Simplicius - On Aristotle's 'Physics' 9.145.1- |
| 1792 | He taught that there are two elements, fire the maker, and earth the matter [Parmenides, by Diog. Laertius] |
| Full Idea: He taught that there were two elements, fire and earth; and that one of them occupies the place of the maker, the other that of the matter. | |
| From: report of Parmenides (fragments/reports [c.474 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Pa.2 |
| 16954 | Generalised talk of 'natural kinds' is unfortunate, as they vary too much [Dummett] |
| Full Idea: In my view, Kripke's promotion of 'natural kinds', coverning chemical substances and animal and plant species, is unfortunate, since these are rather different types of things, and words used for them behave differently. | |
| From: Michael Dummett (Could There Be Unicorns? [1983], 2) | |
| A reaction: My view is that the only significant difference among natural kinds is their degree of stability in character. Presumably particles, elements and particular molecules are fairly invariant, but living things evolve. |
| 5115 | It is feeble-minded to look for explanations of everything being at rest [Aristotle on Parmenides] |
| Full Idea: For people to ignore the evidence of their senses and look for an explanation for everything being at rest is feeble-minded. | |
| From: comment on Parmenides (fragments/reports [c.474 BCE]) by Aristotle - Physics 253a32 | |
| A reaction: Not exactly an argument, but an interestingly robust assertion of commonsense against dodgy arguments. Aristotle is not exactly an empiricist, but he is on that side of the fence. |
| 13217 | The void can't exist, and without the void there can't be movement or separation [Parmenides, by Aristotle] |
| Full Idea: Some philosophers thought what is must be one and immovable. The void, they say, is not: but unless there is a void what is cannot be moved, nor can it be many, since there is nothing to keep things apart. | |
| From: report of Parmenides (fragments/reports [c.474 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 325a06 | |
| A reaction: Somehow this doesn't seem very persuasive any more! I suppose we would distinguish various degrees of void, and assert the existence of sufficient void to allow movement and separation. We must surely agree that total nothingness doesn't exist. |
| 22918 | What could have triggered the beginning [of time and being]? [Parmenides] |
| Full Idea: What need would have aroused it later or sooner, starting from nothing to come into being? | |
| From: Parmenides (fragments/reports [c.474 BCE]), quoted by Robin Le Poidevin - Travels in Four Dimensions 02 'Everything' | |
| A reaction: [Barnes 1982:178] This remains an excellent question. The last I heard was a 'quantum fluctuation', but that seems to be an event, which therefore needs time. |
| 1791 | He was the first person to say the earth is spherical [Parmenides, by Diog. Laertius] |
| Full Idea: He was the first person who asserted that the earth was of a spherical form. | |
| From: report of Parmenides (fragments/reports [c.474 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Pa.2 |
| 1794 | He was the first to discover the identity of the Morning and Evening Stars [Parmenides, by Diog. Laertius] |
| Full Idea: He appears to have been the first to discover that Hesperus and Lucifer were the same star. | |
| From: report of Parmenides (fragments/reports [c.474 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Pa.3 | |
| A reaction: This is the famous example used by Frege to discuss reference and meaning. |